Question

PROVE THAT IN A RIGHT ANGLE TRIANGLE THE HYPOTENUSE IS THE LONGEST SIDE

Answer 1

Simple largest angle's opposite is the largest

Then 90° is the largest angle then its opposite side is always hypotenuse.

So hypotenuse is the longest side.

Answer 2

In the given triangle ABC,

Angle B = 90°

Hence Angle A + Angle C = 180°- 90°  ...(Sum of all angles of the triangle are 180°)

Therefore Angle B is the greater angle than Angle A and Angle C. [Angle A>Angle C ]  

We know that, Side opposite to greater angle is always longer.

Therefore, Side opposite to angle B is AC

.

[AC > BC and AC > AB]

That is AC is the longest side..

[AC is the hypotenuse] ..